This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Resolve each force into its x and y components. We will use the standard convention where angles are measured counter-clockwise from the positive x-axis. Force 1 (F_1 = 300 N): The angle with the negative x-axis is 40^. So, the angle from the positive x-axis is 180^ - 40^ = 140^. F_1x = 300 (140^) = 300(-0.7660) = -229.80 N F_1y = 300 (140^) = 300(0.6428) = 192.84 N Force 2 (F_2 = 400 N): The angle with the positive x-axis is 60^. F_2x = 400 (60^) = 400(0.5) = 200.00 N F_2y = 400 (60^) = 400(0.8660) = 346.40 N Force 3 (F_3 = 300 N): This force acts along the positive x-axis, so its angle is 0^. F_3x = 300 (0^) = 300(1) = 300.00 N F_3y = 300 (0^) = 300(0) = 0 N Force 4 (F_4 = 200 N): This force acts along the negative y-axis, so its angle is 270^. F_4x = 200 (270^) = 200(0) = 0 N F_4y = 200 (270^) = 200(-1) = -200.00 N Step 2: Sum the x-components ( F_x). F_x = F_1x + F_2x + F_3x + F_4x F_x = -229.80 N + 200.00 N + 300.00 N + 0 N F_x = 270.20 N Step 3: Sum the y-components ( F_y). F_y = F_1y + F_2y + F_3y + F_4y F_y = 192.84 N + 346.40 N + 0 N - 200.00 N F_y = 339.24 N Step 4: Calculate the magnitude of the resultant force (R). R = sqrt(( F_x)^2 + ( F_y)^2) R = sqrt((270.20 N))^2 + (339.24 N)^2 R = sqrt(73008.04 N)^2 + 115083.7776 N^2 R = sqrt(188091.8176 N)^2 R ≈ 433.695 N Step 5: Calculate the direction of the resultant force (). = (( F_y)/( F_x)) = (339.24 N270.20 N) = (1.2555) ≈ 51.46^ Since both F_x and F_y are positive, the resultant force is in the first quadrant, and the angle is measured counter-clockwise from the positive x-axis. The resultant force is 433.7 N at an angle of 51.46^ from the positive x-axis. Send me the next one 📸